Neighborhood rough set with neighborhood equivalence relation for feature selection

Feature selection of the neighborhood rough set is an important step in preprocessing the data and improving classification performance. Neighborhood granules form the basis for neighborhood rough set learning and reasoning, but granules typically have overlap, which will cause sample classification uncertainty or repeatability. For this reason, a new notion of neighborhood equivalence relation is used in this paper. Neighborhood equivalence granules solve the above problems, those granules are usually finer than that of the classical neighborhood rough set. In this paper, the neighborhood relation in traditional neighborhood rough set is replaced by neighborhood equivalence relation. Based on neighborhood equivalence relation, a Neighborhood rough set Model based on neighborhood Equivalence Relation (NMER) is proposed. We also introduce the properties of NMER and explain the significance of features. Based on the proposed NMER, a feature selection algorithm is also designed. The reduction results on twelve datasets show that the proposed feature selection algorithm can select main and useful features, confirming the effectiveness of the algorithm.